Predictive Science Academic Alliances Program (PSAAP) Technical White Paper Turbulent Mixing and Hydrodynamics

Abstract

The design of efficient, high-gain capsules for inertial confinement fusion (ICF) and the modeling of supernova implosions and explosions requires a detailed understanding of the consequences of material interpenetration, hydrodynamic instabilities and mixing at molecular (or atomic) scales arising from perturbations at material interfaces, i.e., the Rayleigh-Taylor, Richtmyer-Meshkov and Kelvin-Helmholtz instabilities (buoyancy-, shock- and shear-induced instabilities, respectively). From a computational point of view, this requires the development of models for hydrodynamic instability growth from initial perturbations through the weakly- and strongly-nonlinear phases, and finally, to the late-time turbulent regime. In particular, modeling these processes completely and accurately is critical for demonstrating the feasibility and potential success of contemporary ICF capsule designs. A predictive computational capability for the effects of turbulent mass, momentum, energy and species transport, as well as material mixing, on the thermonuclear fusion process in ICF entails the development of turbulent transport and mixing or subgrid-scale models based on statistically-averaged or filtered evolution equations, respectively. The former models are typically referred to as Reynolds-averaged Navier-Stokes (RANS) (and related) models and the latter are referred to as large-eddy simulation (LES) models. The strong nonlinearity of the equations describing the hydrodynamics, thermodynamics, material properties and other multi-scale phenomena, together with the formal ensemble averaging or filtering procedure, introduce correlations of strongly-fluctuating fields and other a priori unclosed quantities that must be explicitly modeled to close the set of equations describing the implosion dynamics and burning of an ICF capsule.